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Validation Case: 3D Triaxial Displacement Secondary Creep (NAFEMS Test 6(b))

This validation case belongs to solid mechanics. The aim of this test case is to validate the following parameter:

  • creep material behavior
  • standard and reduced integration elements
  • automatic time stepping

The simulation results were compared to the results presented in [NAFEMS]\(^1\).


The geometry consists of a cube with edge length \(l\) = 0.1 \(m\).

geometry of the cube used in secondary creep validation case
Figure 1: Cube geometry

The coordinates for the points in the cube geometry are as tabulated below:

Table 1: Cube dimensions in meters

Analysis Type and Mesh

Tool Type: Code Aster

Analysis Type: Nonlinear static

Mesh and Element Types: The meshes for cases A through D are second-order hexahedral one-element meshes. They were created locally and imported to SimScale. For cases E through H, the standard algorithm was used to generate a second-order tetrahedral mesh.

CaseMesh TypeNumber of NodesCreep FormulationElement Type
A2nd order hexahedral20NortonStandard
B2nd order hexahedral20NortonReduced integration
C2nd order hexahedral20Time HardeningStandard
D2nd order hexahedral20Time HardeningReduced integration
E2nd order standard235NortonStandard
F2nd order standard235NortonReduced integration
G2nd order standard235Time HardeningStandard
H2nd order standard235Time HardeningReduced integration
Table 2: Case overview

Find below the standard mesh used for cases E through H:

generated second order mesh in simscale which has 235 nodes for secondary creep validation
Figure 2: Generated second order mesh with SimScale for cases E-H

Simulation Setup


  • Steel (linear elastic)
    • Isotropic: \(E\) = 200 \(GPa\)
    • \(\nu\) = 0.3
    • \(\rho\) = 7870 \(kg/m³\)
    • Creep formulation:

Boundary Conditions:

  • Constraints:
    • Fixed value:
      • Face ADEH: \(d_x\) = 0 \(m\)
      • Face ABFE: \(d_y\) = 0 \(m\)
      • Face ABCD: \(d_z\) = 0 \(m\)
    • Displacement in x-direction
      • Face BCGF: \(d_x\) = 0.3 \(mm\)
    • Displacement in y-direction
      • Face CDHG: \(d_y\) = 0.2 \(mm\)
    • Displacement in z-direction
      • Face EFGH: \(d_z\) =0.1 \(mm\)

Advanced Automatic Time Stepping

For all cases, the following advanced automatic time stepping settings were defined under Simulation control:

  • Retiming event: Field change
  • Target field component: Internal variable V1 (accumulated unelastic strain)
  • Threshold value: 0.00005
  • Timestep calculation: Mixed
  • Field change target: 0.00004

Result Comparison

The secondary creep movement validation is done by comparing the stress (\(\sigma_{xx}\)) after a creep time of 1000 hours. Below you will find the SimScale and reference results from [NAFEMS]\(^1\):

CaseNAFEMS R27 [MPa]SimScale [MPa]Error [%]
Table 3: Stress comparison

The displacement of the geometry can be seen below:

visualization of displacement of a cube
Figure 3: Displacement visualization


If you still encounter problems validating your simulation, then please post the issue on our forum or contact us.

Last updated: June 27th, 2020